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The maximum number of edges in a n node undirected graph without self loops is n 2 frac n n 1 2 n 1 frac n 1 n 2 | Graph Connectivity | 72 |
The 2 n vertices of a graph G corresponds to all subsets of a set of size n for n geq 6 Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements The number of connected components in G is n n 2 2 frac n 2 frac 2 n n | Graph Connectivity | 72 |
Let G be an arbitrary graph with n nodes and k components If a vertex is removed from G the number of components in the resultant graph must necessarily lie down between k and n k 1 and k 1 k 1 and n 1 k 1 and n k | Graph Connectivity | 72 |
Let G be a directed graph whose vertex set is the set of numbers from 1 to 100 There is an edge from a vertex i to a vertex j iff either j i 1 or j 3i The minimum number of edges in a path in G from vertex 1 to vertex 100 is 4 7 23 99 | Graph Connectivity | 72 |
Let G be a connected undirected graph A cut in G is a set of edges whose removal results in G being broken into two or more components which are not connected with each other The size of a cut is called its cardinality A min cut of G is a cut in G of minimum cardinality Consider the following graph Which of the following sets of edges is a cut left A B E F B D A E A D right left B D C F A B right What is cardinality of min cut in this graph Prove that if a connected undirected graph G with n vertices has a min cut of cardinality k then G has at least left frac n imes k 2 right edges | Graph Connectivity | 72 |
If all the edge weights of an undirected graph are positive then any subset of edges that connects all the vertices and has minimum total weight is a Hamiltonian cycle grid hypercube tree | Graph Connectivity | 72 |
G is a simple undirected graph Some vertices of G are of odd degree Add a node v to G and make it adjacent to each odd degree vertex of G The resultant graph is sure to be regular complete Hamiltonian Euler | Graph Connectivity | 72 |
Consider an undirected graph G where self loops are not allowed The vertex set of G is i j mid1 leq i leq 12 1 leq j leq 12 There is an edge between a b and c d if a c leq 1 and b d leq 1 The number of edges in this graph is______ | Graph Connectivity | 72 |
The number of articulation points of the following graph is 0 1 2 3 | Graph Connectivity | 72 |
Let G V E be a graph Define bar G to be V bar E where for all u v in V u v in bar E if and only if u v otin E Then which of the following is true bar G is always connected bar G is connected if G is not connected At least one of G and bar G connected G is not connected or bar G is not connected | Graph Connectivity | 72 |
Consider a simple connected graph G with n vertices and n edges n gt 2 Then which of the following statements are true G has no cycles The graph obtained by removing any edge from G is not connected G has at least one cycle The graph obtained by removing any two edges from G is not connected None of the above | Graph Connectivity | 72 |
A cycle on n vertices is isomorphic to its complement The value of n is _____ | Graph Isomorphism | 73 |
Which of the following graphs is isomorphic to | Graph Isomorphism | 73 |
How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 | Graph Matching | 74 |
Choose the correct alternatives More than one may be correct A graph is planar if and only if It does not contain subgraphs homeomorphic to k_ 5 and k_ 3 3 It does not contain subgraphs isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph homeomorphic to k_ 5 or k_ 3 3 | Graph Planarity | 75 |
Answer the following Which of the following graphs is are planner see Fig 2 | Graph Planarity | 75 |
What is the size of the smallest MIS Maximal Independent Set of a chain of nine nodes 5 4 3 2 | Graphs | 76 |
Let G V E be a directed graph where V is the set of vertices and E the set of edges Then which one of the following graphs has the same strongly connected components as G G_1 V E_1 where E_1 left u v mid u v otin E right G_2 V E_2 where E_2 left u v mid v u in E right G_3 V E_3 where E_3 u v mid there is a path of length leq2 from u to v in E G_4 V_4 E where V_4 is the set of vertices in G which are not isolated | Graphs | 76 |
Let G be the graph with 100 vertices numbered 1 to 100 Two vertices i and j are adjacent if vert i j vert 8 or vert i j vert 12 The number of connected components in G is 8 4 12 25 | Graphs | 76 |
How many edges can there be in a forest with p components having n vertices in all | Graphs | 76 |
Consider the weighted undirected graph with 4 vertices where the weight of edge i j is given by the entry W_ ij in the matrix W W begin bmatrix 0 amp 2 amp 8 amp 5 2 amp 0 amp 5 amp 8 8 amp 5 amp 0 amp x 5 amp 8 amp x amp 0 end bmatrix The largest possible integer value of x for which at least one shortest path between some pair of vertices will contain the edge with weight x is ___________ | Graphs | 76 |
G is a graph on n vertices and 2n 2 edges The edges of G can be partitioned into two edge disjoint spanning trees Which of the following is NOT true for G For every subset of k vertices the induced subgraph has at most 2k 2 edges The minimum cut in G has at least 2 edges There are at least 2 edge disjoint paths between every pair of vertices There are at least 2 vertex disjoint paths between every pair of vertices | Graphs | 76 |
Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 | Gray Code | 77 |
The set 1 2 4 7 8 11 13 14 is a group under multiplication modulo 15 the inverses of 4 and 7 are respectively a 3 and 13 b 2 and 11 c 4 and 13 d 8 and 14 | Groups | 78 |
The following is the incomplete operation table of a 4 element group e a b c e e a b c a a b c e b c The last row of the table is c a e b c b a e c b e a c e a b | Groups | 78 |
Let S 0 1 2 3 4 5 6 7 and u2297 denote multiplication modulo 8 that is x u2297 y xy mod 8 Prove that 0 1 u2297 is not a group Write 3 distinct groups G u2297 where G u2282 S and G has 2 elements | Groups | 78 |
Let left Z right be an algebraic structure where Z is the set of integers and the operation is defined by n m max n m Which of the following statements is true for u00a0 left Z right left Z right is a monoid left Z right is an Abelian group left Z right is a group None of the above | Groups | 78 |
Let left p q right be a semigroup where p p q Show that p q q p and q q q | Groups | 78 |
If G is a group of even order then show that there exists an element a u2260e e the identity in G such that a 2 e | Groups | 78 |
Consider the set Sigma of all strings over the alphabet Sigma 0 1 Sigma with the concatenation operator for strings does not form a group forms a non commutative group does not have a right identity element forms a group if the empty string is removed from Sigma | Groups | 78 |
Consider the set H of all 3 3 matrices of the type left begin array ccc a amp f amp e 0 amp b amp d 0 amp 0 amp c end array right where a b c d e and f are real numbers and abc u2260 0 under the matrix multiplication operation the set H is a group a monoid but not a group a semi group but not a monoid neither a group nor a semi group | Groups | 78 |
Which of the following statements is false The set of rational numbers is an abelian group under addition The set of integers in an abelian group under addition The set of rational numbers form an abelian group under multiplication The set of real numbers excluding zero is an abelian group under multiplication | Groups | 78 |
Some group G o is known to be abelian Then which one of the following is true for G g g 1 ext for every g in G g g 2 ext for every g in G goh 2 g 2oh 2 ext for every g h in G G is of finite order | Groups | 78 |
Let G_1 and G_2 be subgroups of a group G Show that G_1 cap G_2 is also a subgroup of G Is G_1 cup G_2 always a subgroup of G | Groups | 78 |
Let A be the set of all non singular matrices over real number and let be the matrix multiplication operation Then A is closed under but langle A rangle is not a semigroup langle A rangle is a semigroup but not a monoid langle A rangle is a monoid but not a group langle A rangle is a a group but not an abelian group | Groups | 78 |
Let A be a semigroup Furthermore for every a and b in A if a eq b then a b eq b a Show that for every a in A a a a Show that for every a b in A a b a a Show that for every a b c in A a b c a c | Groups | 78 |
Consider the set of integers 1 2 3 4 6 8 12 24 together with the two binary operations LCM lowest common multiple and GCD greatest common divisor Which of the following algebraic structures does this represent group ring field lattice | Groups | 78 |
A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ | Half Adder | 79 |
The keys 12 18 13 2 3 23 5 and 15 are inserted into an initially empty hash table of length 10 using open addressing with hash function h k k mod 10 and linear probing What is the resultant hash table A B C D 0 1 2 2 3 23 4 5 15 6 7 8 18 9 0 1 2 12 3 13 4 5 5 6 7 8 18 9 0 1 2 12 3 13 4 2 5 3 6 23 7 5 8 18 9 15 0 1 2 2 12 3 13 3 23 4 5 5 15 6 7 8 18 9 | Hashing | 80 |
Insert the characters of the string K R P C S N Y T J M into a hash table of size 10 Use the hash function h x ord x u2013 ord a 1 mod 10 and linear probing to resolve collisions Which insertions cause collisions Display the final hash table | Hashing | 80 |
Given the following input 4322 1334 1471 9679 1989 6171 6173 4199 and the hash function x mod 10 which of the following statements are true 9679 1989 4199 hash to the same value 1471 6171 hash to the same value All elements hash to the same value Each element hashes to a different value I only II only I and II only III or IV | Hashing | 80 |
Consider a hash table with n buckets where external overflow chaining is used to resolve collisions The hash function is such that the probability that a key value is hashed to a particular bucket is frac 1 n The hash table is initially empty and K distinct values are inserted in the table What is the probability that bucket number 1 is empty after the K th insertion What is the probability that no collision has occurred in any of the K insertions What is the probability that the first collision occurs at the K th insertion | Hashing | 80 |
Consider a hash table with 9 slots The hash function is h k k mod 9 The collisions are resolved by chaining The following 9 keys are inserted in the order 5 28 19 15 20 33 12 17 10 The maximum minimum and average chain lengths in the hash table respectively are 3 0 and 1 3 3 and 3 4 0 and 1 3 0 and 2 | Hashing | 80 |
Consider a hash table with 100 slots Collisions are resolved using chaining Assuming simple uniform hashing what is the probability that the first 3 slots are unfilled after the first 3 insertions 97 imes 97 imes 97 100 3 99 imes 98 imes 97 100 3 97 imes 96 imes 95 100 3 97 imes 96 imes 95 3 imes 100 3 | Hashing | 80 |
Consider a hash table of size seven with starting index zero and a hash function 3x 4 mod 7 Assuming the hash table is initially empty which of the following is the contents of the table when the sequence 1 3 8 10 is inserted into the table using closed hashing Note that u2212 denotes an empty location in the table 8 u2212 u2212 u2212 u2212 u2212 10 1 8 10 u2212 u2212 u2212 3 1 u2212 u2212 u2212 u2212 u2212 3 1 10 8 u2212 u2212 u2212 3 | Hashing | 80 |
Consider a hash table of size 11 that uses open addressing with linear probing Let h k k mod 11 be the hash function used A sequence of records with keys 43 36 92 87 11 4 71 13 14 is inserted into an initially empty hash table the bins of which are indexed from zero to ten What is the index of the bin into which the last record is inserted 3 4 6 7 | Hashing | 80 |
Consider a hash function that distributes keys uniformly The hash table size is 20 After hashing of how many keys will the probability that any new key hashed collides with an existing one exceed 0 5 5 6 7 10 | Hashing | 80 |
A hash table with ten buckets with one slot per bucket is shown in the following figure The symbols S1 to S7 initially entered using a hashing function with linear probing The maximum number of comparisons needed in searching an item that is not present is 4 5 6 3 | Hashing | 80 |
A hash table of length 10 uses open addressing with hash function h k k mod 10 and linear probing After inserting 6 values into an empty hash table the table is shown as below 0 1 2 42 3 23 4 34 5 52 6 46 7 33 8 9 Which one of the following choices gives a possible order in which the key values could have been inserted in the table 46 42 34 52 23 33 34 42 23 52 33 46 46 34 42 23 52 33 42 46 33 23 34 52 | Hashing | 80 |
A hash table of length 10 uses open addressing with hash function h k k mod 10 and linear probing After inserting 6 values into an empty hash table the table is shown as below 0 1 2 42 3 23 4 34 5 52 6 46 7 33 8 9 How many different insertion sequences of the key values using the same hash function and linear probing will result in the hash table shown above 10 20 30 40 | Hashing | 80 |
A hash table contains 10 buckets and uses linear probing to resolve collisions The key values are integers and the hash function used is key 10 If the values 43 165 62 123 142 are inserted in the table in what location would the key value 142 be inserted 2 3 4 6 | Hashing | 80 |
An advantage of chained hash table external hashing over the open addressing scheme is Worst case complexity of search operations is less Space used is less Deletion is easier None of the above | Hashing | 80 |
The minimum number of interchanges needed to convert the array into a max heap is 89 19 40 17 12 10 2 5 7 11 6 9 70 0 1 2 3 | Heap | 81 |
The elements 32 15 20 30 12 25 16 are inserted one by one in the given order into a maxHeap The resultant maxHeap is | Heap | 81 |
Statement for Linked Answer Questions 76 amp 77 A 3 ary max heap is like a binary max heap but instead of 2 children nodes have 3 children A 3 ary heap can be represented by an array as follows The root is stored in the first location a 0 nodes in the next level from left to right is stored from a 1 to a 3 The nodes from the second level of the tree from left to right are stored from a 4 location onward An item x can be inserted into a 3 ary heap containing n items by placing x in the location a n and pushing it up the tree to satisfy the heap property 77 Suppose the elements 7 2 10 and 4 are inserted in that order into the valid 3 ary max heap found in the previous question Q 76 Which one of the following is the sequence of items in the array representing the resultant heap 10 7 9 8 3 1 5 2 6 4 10 9 8 7 6 5 4 3 2 1 10 9 4 5 7 6 8 2 1 3 10 8 6 9 7 2 3 4 1 5 | Heap | 81 |
Statement for Linked Answer Questions 76 amp 77 A 3 ary max heap is like a binary max heap but instead of 2 children nodes have 3 children A 3 ary heap can be represented by an array as follows The root is stored in the first location a 0 nodes in the next level from left to right is stored from a 1 to a 3 The nodes from the second level of the tree from left to right are stored from a 4 location onward An item x can be inserted into a 3 ary heap containing n items by placing x in the location a n and pushing it up the tree to satisfy the heap property 76 Which one of the following is a valid sequence of elements in an array representing 3 ary max heap 1 3 5 6 8 9 9 6 3 1 8 5 9 3 6 8 5 1 9 5 6 8 3 1 | Heap | 81 |
In a min heap with n elements with the smallest element at the root the 7 th smallest element can be found in time Theta n log n Theta n Theta log n Theta 1 | Heap | 81 |
In a binary max heap containing n numbers the smallest element can be found in time O n O log n O log log n O 1 | Heap | 81 |
Consider the process of inserting an element into a Max Heap where the Max Heap is represented by an array Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element the number of comparisons performed is Theta log_2n Theta log_2 log_2n Theta n Theta n log_2n | Heap | 81 |
Consider any array representation of an n element binary heap where the elements are stored from index 1 to index n of the array For the element stored at index i of the array i leq n the index of the parent is i 1 lfloor frac i 2 rfloor lceil frac i 2 rceil frac i 1 2 | Heap | 81 |
Consider a binary max heap implemented using an array Which one of the following array represents a binary max heap left 25 12 16 13 10 8 14 right left 25 14 13 16 10 8 12 right left 25 14 16 13 10 8 12 right left 25 14 12 13 10 8 16 right | Heap | 81 |
An operator delete i for a binary heap data structure is to be designed to delete the item in the i th node Assume that the heap is implemented in an array and i refers to the i th index of the array If the heap tree has depth d number of edges on the path from the root to the farthest leaf then what is the time complexity to re fix the heap efficiently after the removal of the element O 1 O d but not O 1 O 2 d but not O d O d 2 d but not O 2 d | Heap | 81 |
An array X of n distinct integers is interpreted as a complete binary tree The index of the first element of the array is 0 If only the root node does not satisfy the heap property the algorithm to convert the complete binary tree into a heap has the best asymptotic time complexity of O n O log n O n log n O n log log n | Heap | 81 |
An array of integers of size n can be converted into a heap by adjusting the heaps rooted at each internal node of the complete binary tree starting at the node left lfloor n 1 2 right rfloor and doing this adjustment up to the root node root node is at index 0 in the order left lfloor n 1 2 right rfloor left lfloor n 3 2 right rfloor 0 The time required to construct a heap in this manner is O log n O n O n log log n O n log n | Heap | 81 |
A priority queue is implemented as a Max Heap Initially it has 5 elements The level order traversal of the heap is 10 8 5 3 2 Two new elements 1 and 7 are inserted into the heap in that order The level order traversal of the heap after the insertion of the elements is 10 8 7 5 3 2 1 10 8 7 2 3 1 5 10 8 7 1 2 3 5 10 8 7 3 2 1 5 | Heap | 81 |
In binary tree a full node is defined to be a node with 2 children Use induction on the height of the binary tree to prove that the number of full nodes plus one is equal to the number of leaves Draw the min heap that results from insertion of the following elements in order into an initially empty min heap 7 6 5 4 3 2 1 Show the result after the deletion of the root of this heap | Heap | 81 |
The language left a mb nc m n mid m n geq1 right is regular context free but not regular context sensitive but not context free type 0 but not context sensitive | Identify Class Language | 82 |
The language L left 0 i21 i mid i geq 0 right over the alphabet left 0 1 2 right is not recursive is recursive and is a deterministic CFL is a regular language is not a deterministic CFL but a CFL | Identify Class Language | 82 |
The language accepted by a Pushdown Automaton in which the stack is limited to 10 items is best described as Context free Regular Deterministic Context free Recursive | Identify Class Language | 82 |
The language 0 n 1 n 2 n mid 1 leq n leq 10 6 is regular context free but not regular context free but its complement is not context free not context free | Identify Class Language | 82 |
Show that the Turing machines which have a read only input tape and constant size work tape recognize precisely the class of regular languages | Identify Class Language | 82 |
Multiple choices may be correct If L1 is context free language and L2 is a regular language which of the following is are false L1 L2 is not context free L1 cap L2 is context free sim L1 is context free sim L2 is regular | Identify Class Language | 82 |
Let L_1 be a regular language L_2 be a deterministic context free language and L_3 a recursively enumerable but not recursive language Which one of the following statements is false L_1 cap L_2 is a deterministic CFL L_3 cap L_1 is recursive L_1 cup L_2 is context free L_1 cap L_2 cap L_3 is recursively enumerable | Identify Class Language | 82 |
Let L denote the languages generated by the grammar S o 0S0 mid 00 Which of the following is TRUE L 0 L is regular but not 0 L is context free but not regular L is not context free | Identify Class Language | 82 |
Let L be a regular language and M be a context free language both over the alphabet u03a3 Let L c and M c denote the complements of L and M respectively Which of the following statements about the language L c cup M c is TRUE It is necessarily regular but not necessarily context free It is necessarily context free It is necessarily non regular None of the above | Identify Class Language | 82 |
Let L L_1 cap L_2 where L_1 and L_2 are languages as defined below L_1 left a m b mca nb n mid m n geq 0 right L_2 left a i b j c k mid i j k geq 0 right Then L is Not recursive Regular Context free but not regular Recursively enumerable but not context free | Identify Class Language | 82 |
For s in 0 1 let d s denote the decimal value of s e g d 101 5 Let L left s in 0 1 mid d s ext mod 5 2 ext and d s ext mod 7 eq 4 right Which one of the following statements is true L is recursively enumerable but not recursive L is recursive but not context free L is context free but not regular L is regular | Identify Class Language | 82 |
Consider the languages L_1 left a nb nc m mid n m gt 0 right and L_2 left a nb mc m mid n m gt 0 right Which one of the following statements is FALSE L_1 cap L_2 is a context free language L_1 cup L_2 is a context free language L_1 ext and L_2 are context free languages L_1 cap L_2 is a context sensitive language | Identify Class Language | 82 |
Consider the following languages L_1 a i b j c k mid i j k geq 1 L_2 a i b j mid j 2i i geq 0 Which of the following is true L_1 is not a CFL but L_2 is L_1 cap L_2 varnothing and L_1 is non regular L_1 cup L_2 is not a CFL but L_2 is There is a 4 state PDA that accepts L_1 but there is no DPDA that accepts L_2 | Identify Class Language | 82 |
a Given a set S left x mid ext there is an x block of 5 s in the decimal expansion of pi right Note x block is a maximal block of x successive 5 s Which of the following statements is true with respect to S No reason to be given for the answer S is regular S is recursively enumerable S is not recursively enumerable S is recursive b Given that a language L_1 is regular and and that the language L_1 cup L_2 is regular is the language L_2 always regular Prove your answer | Identify Class Language | 82 |
The following bit pattern represents a floating point number in IEEE 754 single precision format 1 10000011 101000000000000000000000 The value of the number in decimal form is 10 13 26 None of the above | Ieee Representation | 83 |
The decimal value 0 5 in IEEE single precision floating point representation has fraction bits of 000 dots 000 and exponent value of 0 fraction bits of 000 dots 000 and exponent value of u22121 fraction bits of 100 dots 000 and exponent value of 0 no exact representation | Ieee Representation | 83 |
In the IEEE floating point representation the hexadecimal value 0 ext x 00000000 corresponds to The normalized value 2 127 The normalized value 2 126 The normalized value 0 The special value 0 | Ieee Representation | 83 |
There are five records in a database Name Age Occupation Category Rama 27 CON A Abdul 22 ENG A Jennifer 28 DOC B Maya 32 SER D Dev 24 MUS C There is an index file associated with this and it contains the values 1 3 2 5 and 4 Which one of the fields is the index built from Age Name Occupation Category | Indexing | 84 |
In a B Tree if the search key value is 8 bytes long the block size is 512 bytes and the pointer size is 2 B then the maximum order of the B Tree is ____ | Indexing | 84 |
Consider a relational table r with sufficient number of records having attributes A_1 A_2 dots A_n and let 1 leq p leq n Two queries Q1 and Q2 are given below Q1 pi_ A_1 dots A_p left sigma_ A_p c left r right right where c is a constant Q2 pi_ A_1 dots A_p left sigma_ c_1 leq A_p leq c_2 left r right right where c_1 and c_2 are constants The database can be configured to do ordered indexing on A_p or hashing on A_p Which of the following statements is TRUE Ordered indexing will always outperform hashing for both queries Hashing will always outperform ordered indexing for both queries Hashing will outperform ordered indexing on Q1 but not on Q2 Hashing will outperform ordered indexing on Q2 but not on Q1 | Indexing | 84 |
Consider a file of 16384 records Each record is 32 bytes long and its key field is of size 6 bytes The file is ordered on a non key field and the file organization is unspanned The file is stored in a file system with block size 1024 bytes and the size of a block pointer is 10 bytes If the secondary index is built on the key field of the file and a multi level index scheme is used to store the secondary index the number of first level and second level blocks in the multi level index are respectively 8 and 0 128 and 6 256 and 4 512 and 5 | Indexing | 84 |
An index is clustered if it is on a set of fields that form a candidate key it is on a set of fields that include the primary key the data records of the file are organized in the same order as the data entries of the index the data records of the file are organized not in the same order as the data entries of the index | Indexing | 84 |
An ext ISAM indexed sequential file consists of records of size 64 bytes each including key field of size 14 bytes An address of a disk block takes 2 bytes If the disk block size is 512 bytes and there are 16 K records compute the size of the data and index areas in terms of number blocks How many levels of ext tree do you have for the index | Indexing | 84 |
A file is organized so that the ordering of the data records is the same as or close to the ordering of data entries in some index Than that index is called Dense Sparse Clustered Unclustered | Indexing | 84 |
A clustering index is defined on the fields which are of type non key and ordering non key and non ordering key and ordering key and non ordering | Indexing | 84 |
Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG | Inference | 85 |
The value of the integral given below is int limits_0 pi x 2 cos x dx 2 pi pi pi 2 pi | Integration | 86 |
Let S sum_ i 3 100 i log_ 2 i and T int_ 2 100 x log_ 2 x dx Which of the following statements is true S gt T S T S lt T and 2S gt T 2S u2264 T | Integration | 86 |
If int limits_0 2 pi x sin x dx k pi then the value of k is equal to ______ | Integration | 86 |
Given i sqrt 1 what will be the evaluation of the definite integral int limits_0 pi 2 dfrac cos x i sin x cos x i sin x dx A 0 B 2 C i D i | Integration | 86 |
Compute the value of large int_ frac 1 pi frac 2 pi frac cos 1 x x 2 dx | Integration | 86 |
int pi 4 _0 1 an x 1 an x dx 0 1 ln 2 1 2 ln 2 | Integration | 86 |
If for non zero x af x bf frac 1 x frac 1 x 25 where a a eq b ext then int_1 2 f x dx is frac 1 a 2 b 2 begin bmatrix a ln 2 25 frac 47b 2 end bmatrix frac 1 a 2 b 2 begin bmatrix a 2 ln 2 25 frac 47b 2 end bmatrix frac 1 a 2 b 2 begin bmatrix a 2 ln 2 25 frac 47b 2 end bmatrix frac 1 a 2 b 2 begin bmatrix a ln 2 25 frac 47b 2 end bmatrix | Integration | 86 |
I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above | Inter Process Communication | 87 |
Subsets and Splits